Standard Deviation, Skewness and Kurtosis

Hello everyone.

Can you please help me confirm that I have well understood the concepts of Standard Deviation, Skewness and Kurtosis based on the following example.

Given the following table for a specific stock:

Holding period Annualized mean return Excess Kurtosis Skewness Standard Deviation

1 month 38.24% 85.14 7.68 0.17

3 months 37.54% 25.64 4.32 0.29

6 months 35.55% 12.21 3.14 0.41

12 months 33.56% 7.44 2.64 0.61

24 months 31.15% 1.43 1.44 0.90

48 months 29.01% 2.03 1.66 1.67

72 months 19.15% -0.72 0.56 1.48

Considerating that transaction costs are not taken into account and only based on return, trading on a monthly basis will generate a greater return.

If I take Standard Deviation, it implies that 1 month trading is also the least risky.

72 months trading has excess kurtosis and skewness close to 0 meaning it is close to a normal distribution.

Theory says investors should go towards positive skewness so here 1 month trading will be our choice.

However excess kurtosis tells that 1 month trading will have the fatest tails implying greater risk which contradicts standard deviation. Skewness for 1 month trading is very high meaning that we are far from normal distribution and that standard deviation should not be taken to seriously.

As a consequence should we say 1 month trading is the most risky strategy?

Thank you for your help

I think investment decisions go further than this, you must consider the investor needs, the term of the her investments, the liquidity, the restrictions… , so relying only in skewness and kurtosis is not sufficient. The ideal investment could be an optimized sharpe with positive skewness and small excess kurtosis, but it is not always a reality I think.

Your numbers are weird: excess kurtosis of 85.14, for example, isn’t possible.

I do not understand the standard deviation numbers either, what is 1.48 ?